Premium
On the mutually non isomorphic ℓ p ( ℓ q ) spaces, II
Author(s) -
Albiac Fernando,
Ansorena José Luis
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300161
Subject(s) - mathematics , isomorphism (crystallography) , locally convex topological vector space , banach space , class (philosophy) , perspective (graphical) , pure mathematics , regular polygon , interpolation space , reflexive space , discrete mathematics , functional analysis , topological space , epistemology , geometry , philosophy , chemistry , crystal structure , biochemistry , gene , crystallography
This note is a companion to the article On the mutually non isomorphicℓ p ( ℓ q )spaces published in this journal, in which P. Cembranos and J. Mendoza showed that { ℓ p ( ℓ q ) : 1 ≤ p , q ≤ ∞ } is a collection of mutually non isomorphic Banach spaces [5]. We now complete the picture by allowing the non‐locally convex relatives to be part of their natural family and see that, in fact, no two members of the extended class { ℓ p ( ℓ q ) : 0 < p , q ≤ ∞ } are isomorphic. Our approach is novel in the sense that we reach the isomorphism obstructions from the perspective of bases techniques and the different convexities of the spaces, both methods being intrinsic to quasi‐Banach spaces.